Question

G use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ. margin of error: $121, confidence level: 95%, σ = $528

Answer 1

The sample size should be 73.

We use the formula

$n=(\frac{z*\sigma}{E})^2$

To find the z-score:
Convert 95% to a decimal:  0.95
Subtract from 1:  1-0.95 = 0.05
Divide by 2:  0.05/2 = 0.025
Subtract from 1:  1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this value goes with a z-score of 1.96.  Using this, our value for σ and our margin of error, we have:
$n=(\frac{1.96(528)}{121})^2=73.15\approx73$